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\begin{equation*}\int\frac{mx+n}{ax^2+bx+c}dx = \frac{m}{2a}\ln\left|ax^2+bx+c\right|+\frac{2an-bm}{a\sqrt{b^2-4ac}}\,\mathrm{artanh}\frac{2ax+b}{\sqrt{b^2-4ac}} \qquad\mbox{(for }4ac-b^2<0\mbox{)}\end{equation*}
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